On the dynamics of competitive dynamical systems via the carrying simplex

主讲人：牛磊 东华大学研究员

时间：2023年5月7日10：30

地点：三号楼332室

举办单位：数理学院

主讲人介绍：牛磊，2016-2019年在芬兰赫尔辛基大学Mat Gyllenberg教授的团队做博士后，2020年至今在东华大学数学系工作, 任研究员。主要研究领域包括单调和竞争动力系统、应用动力系统和生物数学。代表性成果发表在JMPA，Nonlinearity，SIADS，JDE，JMB，DCDS-A，Proc. Roy. Soc. Edinburgh A等。2021年入选上海市海外高层次人才计划。

内容介绍：In this talk, we review the theory of carrying simplex of competitive dynamical systems and some of our results for classical competitive mappings. We then discuss a 3D Lotka-Volterra competition model with seasonal succession. We show that the dynamics of the associated Poincaré map can be classified into 33 classes by an equivalence relation relative to the boundary dynamics. We specially establish an index formula on the carrying simplex, by which we obtain which classes have positive fixed points. In classes 1–18, there is no positive fixed point and every orbit tends to some boundary fixed point. While, for classes 19–33, there exists at least one positive fixed point. We further obtain necessary and sufficient conditions for the uniqueness and nonuniqueness of the positive fixed points when the model has identical intrinsic growth rate and death rate, and then give a complete classification of the global dynamics in this case which has a total of 37 dynamical classes.